Geodesic
On Explicit Bounds in Landau's Theorem. II
Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 559-562

Voir la notice de l'article provenant de la source Cambridge University Press

Quite some years ago a number of mathematicians were interested in obtaining explicit expressions for the bounds in Schottky's and Landau's theorems, specifically numerically évaluable bounds of a particular form. The best bounds of this type in Schottky's theorem were given by the author [3]. For Landau's theorem the chosen form is as follows. Let F(Z) be regular in |Z| < 1, omit the values 0 and 1 and have Taylor expansion about Z = 0 Then Using the same method employed for Schottky's theorem the author showed that one can take K = 5.94. By a slight modification of the author's method Lai [6] gave the further value K = 4.76. 
Jenkins, James A. On Explicit Bounds in Landau's Theorem. II. Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 559-562. doi: 10.4153/CJM-1981-045-1
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[1] 1. Ahlfors, Lars V., Conformai invariants (McGraw-Hill, 1973). Google Scholar

[2] 2. Jenkins, James A. and Morse, Marston, Curve families F* locally the level curves of a pseudoharmonic function, Acta Mathematica 91 (1954), 1–42. Google Scholar

[3] 3. Jenkins, James A., On explicit bounds in Schottkys theorem, Can. J. Math. 7 (1955), 76–82. Google Scholar

[4] 4. Jenkins, James A., On explicit bounds in Landau's theorem, Can. J. Math. 8 (1956), 423–425. Google Scholar

[5] 5. Jenkins, James A., A topological Three Pole Theorem, Indiana University Mathematics Journal 21 (1972), 1013–1018. Google Scholar

[6] 6. Lai, W., Ûber den Satz von Landau, Science Record J+ (1960), 339–342. Google Scholar

[7] 7. Review of [3], Mathematical Reviews 16 (1955), 579. Google Scholar

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